Efficient computation of reachable sets of linear time-invariant systems with inputs

Antoine Girard (1) , Colas Le Guernic (2) , Oded Maler (3)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 ENS-PSL - École normale supérieure - Paris
3 VERIMAG - IMAG - VERIMAG

This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems.

Domaines: Optimisation et contrôle [math.OC]

Antoine Girard, Colas Le Guernic, Oded Maler. Efficient computation of reachable sets of linear time-invariant systems with inputs. Hybrid Systems: Computation and Control, HSCC 2006, Mar 2006, Santa Barbara, United States. pp.257-271, ⟨10.1007/11730637_2⟩. ⟨hal-00171555⟩